Given the following definition of a periodic function:
$$\exists P, P > 0, f(x + P) = f(x)$$
It is possible to argue that $f(x)=k$ ($k$ being a constant) is a periodic function, since you can define $P$ to be any given constant within the real numbers and the definition would be valid. ($f(x + P) = f(x)$ will always be true if $P\in \mathbb R$).
So my question is, can a horizontal line be considered periodic, even when its period is ambiguous?